The present invention relates to feedback control calibration for electrically-powered, motion-producing devices and, more particularly, to a method of and apparatus for calibrating electronically driven actuators to offset the cumulative error of poorly toleranced mechanical components and electronic component irregularities by adjusting the gain in the electronic actuator driver circuit in response to feedback derived from positioning a member moved by the actuator to a predetermined position, sensing the actual position, and adjusting the gain in the actuator driver circuit to correct errors in the positioning of the member.
In mechanical devices such as pen plotters, precision linear motion in an electronic actuator such as a voice coil actuator, solenoid, or DC motor is difficult to achieve under changing operating conditions subject to irregularities (non-linear component response and variable gain) in electronic components and cumulative mechanical tolerances. Where precision linear motion is required such as with the up and down movement of a pen-holding apparatus in a pen plotter, previous methods of achieving precision have been limited to using expensive, precision electronic and mechanical components; fine tuning plotter sub-systems; tightly controlling plotter subsystems; and/or utilizing stabilized operating environments. Use of such approaches increases complexity and associated manufacturing costs. Furthermore, they produce a level of precision limited by the individual precision of each element or sub-system in the plotter. Rather than improve the precision incrementally through the use of precision electronic and mechanical components or tuning and controlling, what is needed is a scheme which can continuously offset the cumulative mechanical errors as well as errors due to electronic irregularities. The result would be electronic actuators for pen plotters, and the like, which are simpler and use less expensive components while maintaining consistent precision performance under changing operating conditions.
Various feedback control systems are, of course, well known in many arts. As depicted in FIG. 1, a typical control system 10 involves a controller 12, drive electronics 14, an actuator 16, a mechanical load 18, and a sensor 20. Data required by the controller 12 is maintained in a storage memory 22. The control algorithm utilized can be a proportional plus derivative (PD) control, which can be represented as: EQU U(s)=Kp*(1+Kd*S)*E(S) (1)
where
S is the Laplace operator, PA1 U(S) is the output of the controller, PA1 K.sub.p is the proportional gain, PA1 K.sub.d is the derivative gain, PA1 E(S) is the error signal. PA1 I(S) is the current output of the drive electronics, PA1 K.sub.a is the gain of the drive electronics PA1 F(S) is the output force of the actuator, PA1 K.sub.t is the force constant of the actuator. PA1 F.sub.d (S) is a disturbance force (spring force or friction), PA1 X(S) is the mechanical displacement, PA1 M is the inertia. PA1 E.sub.1 =X.sub.d -X.sub.1ss PA1 E.sub.2 =X.sub.d -X.sub.2ss PA1 X.sub.d is the desired position (see FIG. 6), PA1 X.sub.1ss is the position response of the mechanical system at steady state with the proportional gain equal to k.sub.p1, PA1 X.sub.2ss is the position response of the mechanical system at steady state with the proportional gain equal to k.sub.p2.
Assuming the drive electronics 14 deliver a current, then the current can be represented as: EQU I(S)=K.sub.a *U(S)
where
The actuator 16 can be represented as: EQU F(S)=K.sub.t *I(S)
where
The mechanical load 18, be it a spring or friction, can be defined as: EQU F(S)-F.sub.d (S)=X(S)/M*S.sup.2
where
The latter is represented in FIG. 2. The overall system gain is constituted by the gain of each block. The gain variation of each block will affect the overall system response.
In actual application, the gain of each block will vary due to factors such as thermal effect, the individual consistency of the components, ambient operating conditions, or other environmental factors. For example, the output of a sensor can vary for the same mechanical displacement as depicted in FIG. 3. At a higher temperature, a sensor will have a steeper rate which means a higher gain. Thermal effect can also affect the gain of other electronic components within the system and the tolerances of mechanical components.
Another effect is the variation of the force constant of the actuator. Typically, a lower force constant results when the temperature of the actuator rises. Also, different actuator types have different force constants. For example, a voice coil type actuator's force constant is nearly fixed except near the fully retracted and fully extended stroke positions as depicted in FIG. 4. However, if a solenoid is used, the force constant is a non-linear function of stroke displacement as depicted in FIG. 5.
The aforementioned variations and irregularities each individually contribute to the system's overall electronic gain and affect the overall system performance.
In a system such as the one shown in FIG. 2, the steady state error for controlling the position of an armature of the actuator 16 is inversely proportional to the overall system gain. For a fixed set of hardware, the overall system gain is proportional to the proportional gain K.sub.p of the controller. For different K.sub.p, there is a relationship: EQU E.sub.1 /E.sub.2 =K.sub.p2 /K.sub.p1
where
Based on this relationship, the overall system gain can be estimated according to the steady state error measurement in order to maintain the overall system gain at a constant level.
Wherefore it is the object of the present invention to provide an inexpensive and simple calibration scheme to offset inherent system irregularities and inaccuracies, which can be employed to ensure precision linear movement in an electronically driven actuator.
It is the further object of this invention to provide a feedback control scheme adapted to produce precision linear movement which can be employed to advantage in relatively inexpensive mechanical devices such as the pen movement mechanism of a pen plotter.
Other objects and benefits of the invention will become apparent to one skilled in the art from the detailed description which follows hereinafter when taken in conjunction with the drawing figures which accompany it.